Herb Garden On A New York, New York, USA Windowsill

I live in NYC and want to start a herb garden in a 24" long x 6" deep x 6" high (60cm X 15cm X 15cm) wooden container. I don't know what herbs to use at this time of year if there is a time of year for herbs. What do you suggest? Would even try tomatoes or another vegetable, but my farm consists of a window sill.

If your windowsill has sun for about 5 hours a day, then you can grow almost any culinary herb you wish. If you want to have perennial herbs survive the winter, you will have to have a South-facing windowsill for them during the winter. Tomatoes would do fine on a sunny windowsill, but with your limited space they might get too big.
On a north-facing windowsill you might be limited to parsley, lovage and mints. With mints be careful to confine them, otherwise your entire tray will soon contain nothing but mint.
If you want to grow chives or French tarragon have them in pots that you sink into the soil-filled tray and take them out in late fall to give them a month of freezing- otherwise they will slowly peter out and die on you.